Anisotropic texture filtering applies a texture at a sampling point in screen space. Calculated texture-filter parameters configure a filter to perform filtering of the texture for the sampling point. The texture for the sampling point is filtered using a filtering kernel having a footprint in texture space determined by the texture-filter parameters. Texture-filter parameters are calculated by generating a first and a second pair of screen-space basis vectors being rotated relative to each other. First and second pairs of texture-space basis vectors are calculated that correspond to the first and second pairs of screen-space basis vectors transformed to texture space under a local approximation of a mapping between screen space and texture space. An angular displacement is determined between a selected pair of the first and second pairs of screen-space basis vectors and screen-space principal axes of a local approximation of the mapping that indicate the maximum and minimum scale factors of the mapping. The angular displacement and the pair of screen-space basis vectors are used to generate texture-space principal axes comprising a major axis associated with the maximum scale factor of the mapping and a minor axis associated with the minimum scale factor of the mapping.